Variable neural networks for adaptive control of nonlinear systems

This paper is concerned with the adaptive control of continuous-time nonlinear dynamical systems using neural networks. A novel neural network architecture, referred to as a variable neural network, is proposed and shown to be useful in approximating the unknown nonlinearities of dynamical systems. In the variable neural networks, the number of basis functions can be either increased or decreased with time, according to specified design strategies, so that the network will not overfit or underfit the data set. Based on the Gaussian radial basis function (GRBF) variable neural network, an adaptive control scheme is presented. The location of the centers and the determination of the widths of the GRBFs in the variable neural network are analyzed to make a compromise between orthogonality and smoothness. The weight-adaptive laws developed using the Lyapunov synthesis approach guarantee the stability of the overall control scheme, even in the presence of modeling error(s). The tracking errors converge to the required accuracy through the adaptive control algorithm derived by combining the variable neural network and Lyapunov synthesis techniques. The operation of an adaptive control scheme using the variable neural network is demonstrated using two simulated example

Trajectory Tracking Error Using Fractional Order PID Control Law for Two‐Link Robot Manipulator via Fractional Adaptive Neural Networks

The problem of trajectory tracking of unknown nonlinear systems of fractional order is solved using fractional order dynamical neural networks. For this purpose, we obtained control laws and laws of adaptive weights online, obtained using the Lyapunov stability analysis methodology of fractional order. Numerical simulations illustrate the obtained theoretical results

Neuroadaptive Model Following Controller Design for a Nonaffine UAV Model

This paper proposes a new model-following adaptive control design technique for nonlinear systems that are nonaffine in control. The adaptive controller uses online neural networks that guarantee tracking in the presence of unmodeled dynamics and/or parameter uncertainties present in the system model through an online control adaptation procedure. The controller design is carried out in two steps: (i) synthesis of a set of neural networks which capture the unmodeled (neglected) dynamics or model uncertainties due to parametric variations and (ii) synthesis of a controller that drives the state of the actual plant to that of a reference model. This method is tested using a three degree of freedom model of a UAV. Numerical results which demonstrate these features and clearly bring out the potential of the proposed approach are presented in this paper

Self-organizing input space for control of structures

We propose a novel type of neural networks for structural control, which comprises an adaptive input space. This feature is purposefully designed for sequential input selection during adaptive identification and control of nonlinear systems, which allows the input space to be organized dynamically, while the excitation is occurring. The neural network has the main advantages of (1) automating the input selection process for time series that are not known a priori; (2) adapting the representation to nonstationarities; and (3) using limited observations. The algorithm designed for the adaptive input space assumes local quasi-stationarity of the time series, and embeds local maps sequentially in a delay vector using the embedding theorem. The input space of the representation, which in our case is a wavelet neural network, is subsequently updated. We demonstrate that the neural net has the potential to significantly improve convergence of a black-box model in adaptive tracking of a nonlinear system. Its performance is further assessed in a full-scale simulation of an existing civil structure subjected to nonstationary excitations (wind and earthquakes), and shows the superiority of the proposed method

Variable Neural Networks for Adaptive Control of Nonlinear Systems

This paper is concerned with the adaptive control of continuous-time nonlinear dynamical systems using neural networks. A novel neural network architecture, is referred to as a variable neural network, is proposed and shown to be useful in approximating the unknown nonlinearities of dynamical systems. In the variable neural networks, the number of basis functions can be either increased or decreased with time according to specified design strategies so that the network will not overfit or underfit the the data set. Based on the Gaussian radial basis function variable neural network, an adaptive control scheme is presented. The location of the centres and the determination of the widths of the Gaussian radial basis functions in the variable neural network are analysed to make a compromise between orthogonality and smoothness. The weight of adaptive laws developed using the Lyapunov synthesis approach guarantee the stability of the overall control scheme, even in the presence of modelling error. The tracking errors converge to the required accuracy through the adaptive control algorithm derived by combining the variable neural network and Lyapunov synthesis techniques. The operation of an adaptive control scheme using the variable neural network is demonstrated using a simulated example

Trajectory Tracking Using Adaptive Fractional PID Control of Biped Robots with Time-Delay Feedback

This paper presents the application of fractional order time-delay adaptive neural networks to the trajectory tracking for chaos synchronization between Fractional Order delayed plant, reference and fractional order time-delay adaptive neural networks. For this purpose, we obtained two control laws and laws of adaptive weights online, obtained using the fractional order Lyapunov-Krasovskii stability analysis methodology. The main methodologies, on which the approach is based, are fractional order PID the fractional order Lyapunov-Krasovskii functions methodology, although the results we obtain are applied to a wide class of non-linear systems, we will apply it in this chapter to a bipedal robot. The structure of the biped robot is designed with two degrees of freedom per leg, corresponding to the knee and hip joints. Since torso and ankle are not considered, it is obtained a 4-DOF system, and each leg, we try to force this biped robot to track a reference signal given by undamped Duffing equation. To verify the analytical results, an example of dynamical network is simulated, and two theorems are proposed to ensure the tracking of the nonlinear system. The tracking error is globally asymptotically stabilized by two control laws derived based on a Lyapunov-Krasovskii functional

Adaptive Predictive Control Using Neural Network for a Class of Pure-feedback Systems in Discrete-time

10.1109/TNN.2008.2000446IEEE Transactions on Neural Networks1991599-1614ITNN